Best Known (33, ∞, s)-Nets in Base 81
(33, ∞, 370)-Net over F81 — Constructive and digital
Digital (33, m, 370)-net over F81 for arbitrarily large m, using
- net from sequence [i] based on digital (33, 369)-sequence over F81, using
- t-expansion [i] based on digital (16, 369)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 16 and N(F) ≥ 370, using
- t-expansion [i] based on digital (16, 369)-sequence over F81, using
(33, ∞, 576)-Net over F81 — Digital
Digital (33, m, 576)-net over F81 for arbitrarily large m, using
- net from sequence [i] based on digital (33, 575)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 33 and N(F) ≥ 576, using
(33, ∞, 2788)-Net in Base 81 — Upper bound on s
There is no (33, m, 2789)-net in base 81 for arbitrarily large m, because
- m-reduction [i] would yield (33, 2787, 2789)-net in base 81, but
- extracting embedded OOA [i] would yield OA(812787, 2789, S81, 2754), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 502725 220984 619956 895141 550174 387866 425949 044061 222978 608663 750785 975612 382182 946257 191702 759555 282969 471790 788268 463532 079201 067072 485959 119546 367581 027459 546243 932454 770774 918916 177272 328607 112561 619883 919787 651392 421684 055968 604336 131698 832485 816011 434428 991378 249978 467454 826994 493621 000824 055673 695479 609485 531146 974454 023584 157043 115034 640471 400694 780289 926906 632432 257421 690530 529801 504266 265949 706751 883536 537276 203967 424404 595057 897961 365496 188765 574884 448851 536317 485085 179343 635057 552234 215653 604503 027459 283471 689513 125397 729741 382820 979964 150775 788256 462255 853378 297717 290358 895211 457252 970158 091945 815241 039932 034860 585563 580325 439973 725845 868115 557370 046351 013392 735658 496491 534905 203068 618365 500304 645280 537606 704765 564794 567971 340008 175924 641428 947722 033732 915680 806322 858688 890535 490375 125012 902290 783046 595563 680354 266560 940866 034946 457241 282718 350430 915189 310046 680000 300476 200266 157732 402888 618759 804137 203012 046577 514414 944866 342296 912049 407736 322779 991654 240809 137480 261330 436255 082862 715386 648654 411615 852959 544522 663675 736099 600385 611257 591808 938230 196024 647909 718189 596370 375139 678784 006948 539290 706528 212360 269301 435189 023205 054957 633840 831015 656577 960971 728682 114001 192491 222177 666541 065199 330308 219668 022893 466211 138392 444409 456199 006618 967420 688703 359732 850581 588914 398993 776862 109073 315592 661146 721466 293753 155444 102833 163681 606211 786227 974852 290746 243404 467541 999958 336135 461325 911956 551725 171417 758272 274377 568865 278031 379731 574760 454525 134795 747658 498807 402660 281243 564548 321224 293142 165174 866776 291293 950677 301072 906653 672661 791846 558658 101796 200205 579989 205469 833903 725416 784013 737530 947089 807738 390162 717254 745942 635867 819047 703499 341181 828200 241702 623236 195259 118498 068669 413617 409809 270451 158548 867729 466054 904947 884413 485803 707867 224412 652952 573293 138792 567914 852289 362674 972349 285188 262632 069087 614795 877188 241152 685156 580893 745430 031626 039375 523070 155317 485963 155465 290363 388953 083903 955040 924550 820679 532442 254554 050726 746989 037431 425092 361043 588328 679656 606872 089014 823551 116005 903486 166312 932538 068856 429958 942800 892527 275605 386278 495378 771146 374654 279348 310264 560005 551982 042096 385927 740255 637413 449448 763222 474927 096541 315529 386575 270712 934606 041561 826227 032172 403397 588426 836978 945876 218319 704399 190524 481619 733415 621214 101518 675337 436847 419271 786792 298755 470797 815056 696310 319644 611592 591174 650528 113245 079752 186623 545360 295555 266518 791622 487643 761051 984043 908815 244709 063108 129988 306873 498782 075736 599959 782543 913805 952857 657430 316656 654230 028165 891910 825022 694061 585025 515506 783295 871272 920055 616555 243899 576917 731298 798552 149223 146146 570160 141302 427347 356340 707935 821140 515550 520119 925822 722254 233799 103887 792558 249008 032663 932351 111033 293989 355033 394739 957540 869244 017556 929706 600414 921594 144245 817819 286272 635471 160820 639990 640790 392969 135551 878703 595410 659188 346712 139645 272077 855821 849656 462269 923572 665219 052359 716579 196220 642043 367674 402619 277813 933870 461725 613675 868679 019797 662665 649365 089287 102967 187474 486317 757484 734484 838293 108159 279290 691187 862774 138613 942847 935212 760608 079533 650973 236566 142015 415315 189359 909332 354053 171260 358655 493048 994956 239328 791852 952865 949645 489871 552665 069822 705702 432306 091492 941573 307253 626306 569833 370940 703530 823018 771423 002540 260156 459537 092210 775924 051633 506500 182392 311697 788651 971696 028466 844452 622846 969757 508707 050184 006073 984226 912650 843930 757017 058320 116858 055169 993221 228132 622054 342067 883699 653343 062356 049330 210983 508268 033738 864929 097750 811727 022950 504599 695818 431891 601304 699264 924929 889623 884819 597461 994961 295243 399026 843907 721977 396534 601885 718607 001877 527731 519003 474291 331091 424027 012624 635055 013016 773393 277427 308319 300274 902160 594809 320176 454382 592364 541131 692386 155401 120454 139199 608700 890639 392824 400874 220994 195519 402660 017182 121362 062182 321465 402705 680891 637287 349934 316646 921407 661241 842481 828638 894000 661201 151043 032452 550177 397866 090010 752800 068035 469513 448236 321807 335665 043236 735151 704756 233807 173967 820738 866978 293588 511048 441516 017320 609988 989064 254653 597139 154173 849406 979349 455091 605454 911981 914166 984367 819969 477224 327444 153059 429565 048521 038346 122074 375716 945195 772858 446065 005336 868774 774184 614358 850078 160441 224165 410166 981496 985662 656314 781355 153348 737476 850488 253642 394842 110791 016078 759836 704004 797198 195604 537585 762861 198252 632634 106551 907626 430907 556417 206452 847924 456233 053128 290651 809825 142372 147610 841621 635833 134261 267040 166452 167694 008561 987711 865823 809824 309440 795261 568050 593246 989768 583947 168675 921727 792330 287518 888217 671539 088329 966308 893298 641868 065406 535109 541709 575620 237465 168813 658098 260984 240677 373761 693615 612303 364226 882313 706934 158712 895495 573220 351077 796506 765312 778000 382222 794539 007959 718626 167962 600554 411072 055631 076922 477887 783675 707693 283228 622967 989486 366701 379125 478082 101833 824598 258010 212962 915081 009193 339488 366370 259833 840585 606736 754688 523280 931106 551877 189977 370963 865380 550355 244035 110008 413300 608962 798232 059643 257838 808949 557384 858678 697141 888002 625700 380976 949276 517084 142991 216874 564795 481593 409144 305034 974315 093567 755135 935674 379757 663928 962177 613369 242115 838909 396139 583594 808917 220799 042104 547141 884083 537826 823887 736952 890780 921943 178960 495640 850113 769884 975413 754727 620780 375711 959009 736612 323760 870635 128295 586255 144886 963751 328498 138328 869317 649503 187447 338252 614593 311686 556806 222980 272336 427963 801014 271917 019070 917745 235065 036287 679687 / 551 > 812787 [i]
- extracting embedded OOA [i] would yield OA(812787, 2789, S81, 2754), but